The probability that a student is not a swimmer is `1/5` . Then the probability that out of five students, four are swimmers is (A) `^5C_4""(4/5)^4""1/5` (B) `(4/5)^4""1/5` (C) `^5C_1 1/5(4/5)^4` (D) None of these

Options

A. `.^(5)C_(4)(4/5)^(4)1/5`
B. `(4/5)^(4)1/5`
C. `.^(5)C_(1)1/5(4/5)^(4)`
D. None of these

Explanation

The process of continuous selection of students which are swimmer is a Bernaulli's experiment. Let `X` represents the number of swimmer students from 5 students.
Now probability of student which is not a swimmers is `q=1/5` and probability of student which is a swimmer.
`p=1-q=1-1/5=4/5`
clearly, `X` is a binomial distribution where
`n=5,p=4/5,q=1/5`
`:.P(X=r)=.^(n)C_(r).p^(r)q^(n-r)=.^(5)C_(r).(4/5)^(r)(1/5)^(5-r)`
`P` (four students are swimmers)
`=P(X=4)=.^(5)C_(4)(4/5)^(4)(1/5)=.^(5)C_(4)(4/5)^(4)1/5`